A company buys 15ft boards and has demand for 10 3ft boards

A company buys 15-ft boards and has demand for 10 3-ft boards, 20 5-ft boards, and 15 8-ft boards. Please formulate an LP to help them decide how to cut the boards while minimizing waste.(cutting stock problem)

Solution

One 8 ft. board can be made from each 15 ft. board .

So number of 8 ft. board need=15 .

So 15 , 7 ft. board remains.

In a 7 ft. boards, one 5 ft board or two 3 ft. can be made.

Waste in two 3 ft board is less(1 ft. ) than one 5 ft board.

So out of 15 , 7 ft. boards, 5 used for 3ft. board

10 , 3ft boards are needed.

10 , 7ft. boards remains.

10, 5 ft. boards can be made from it.

Now we need 10 more , 5 ft. board.

from a 15 ft. board, 3 , 5 ft. board can be made.

So we need 4 more boards. Watage = 9ft.

So we need total 19 , 15ft. boards. Out of which 15 used for 15 , 8ft. boards. wastage =7 ft. boards

From watage of 7ft. boards, 5 used for 10 ,3 ft. boards. watage = 1 ft. each =5ft.

10 used for 10 , 5 ft. boards wastage = 2 ft. each = 20 ft.

4 more 15 ft. boards for remaining 10 , 5ft boards , wastage = 10 ft.

Total wastage =35 ft.